Subgroups — C₁₉×#10942 #18016901

Order 4864.

926 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#419	—	2	2	no	—
16	C₁₉×#419	C₄	1	4	yes	complemented
17	C₂×C₁₉×#103	—	2	2	no	—
18	C₂×C₁₉×#103	—	2	1	no	—
19	C₂×C₁₉×#103	—	2	1	no	—
20	C₂×C₁₉×#103	—	2	2	no	—
21	C₂×C₁₉×#103	C₄	1	4	yes	complemented
22	C₂×C₁₉×#101	—	2	2	no	—
23	C₂×C₁₉×#101	—	2	2	no	—
24	C₂×C₁₉×#101	C₄	1	4	yes	complemented
25	C₁₉×#405	—	2	2	no	—
26	C₁₉×#405	—	2	2	no	—
27	C₂×C₁₉×#97	—	2	1	no	—
28	C₂×C₄×C₈×C₁₉	—	2	1	no	—
29	C₁₉×#343	—	2	2	no	—
30	C₁₉×#341	—	2	2	no	—
31	C₁₉×#340	—	2	2	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
44	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
45	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
66	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
67	C₂²×C₈×C₁₉	—	2	1	no	—
68	C₂²×C₈×C₁₉	—	2	1	no	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₂²×C₈×C₁₉	—	2	1	no	—
73	C₂²×C₈×C₁₉	—	2	1	no	—
74	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
75	C₂²×C₈×C₁₉	D₄	1	2	yes	—
76	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
78	C₁₉×#117	—	2	1	no	—
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	C₂×C₄	1	2	yes	—
81	C₁₉×#117	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₁₉×#103	—	2	4	no	—
92	C₁₉×#103	—	2	4	no	—
93	C₁₉×#103	—	2	8	no	—
94	C₁₉×#101	—	2	8	no	—
95	C₁₉×#97	—	2	4	no	—
96	C₄×C₈×C₁₉	—	2	4	no	—
97	C₂⁴×C₁₉	#41	1	1	yes	characteristic
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	—	4	1	no	—
119	C₂×Q₈×C₁₉	—	4	1	no	—
120	C₂×Q₈×C₁₉	—	4	1	no	—
121	C₂×Q₈×C₁₉	—	4	1	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	—	4	1	no	—
124	C₂×Q₈×C₁₉	—	4	1	no	—
125	C₂×Q₈×C₁₉	C₄²	1	4	yes	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	4	1	no	—
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	—	4	1	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	—	8	2	no	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
152	M₁₆×C₁₉	—	2	2	no	—
153	M₁₆×C₁₉	—	2	2	no	—
154	M₁₆×C₁₉	—	2	2	no	—
155	M₁₆×C₁₉	—	2	2	no	—
156	M₁₆×C₁₉	—	2	2	no	—
157	M₁₆×C₁₉	—	2	2	no	—
158	M₁₆×C₁₉	—	2	2	no	—
159	M₁₆×C₁₉	—	4	1	no	—
160	M₁₆×C₁₉	—	4	1	no	—
161	M₁₆×C₁₉	—	4	1	no	—
162	M₁₆×C₁₉	—	4	1	no	—
163	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	2	2	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	4	1	no	—
178	C₂×C₈×C₁₉	—	4	1	no	—
179	C₂×C₈×C₁₉	—	4	1	no	—
180	C₂×C₈×C₁₉	—	4	1	no	—
181	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
182	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	4	1	no	—
187	C₄⋊C₄×C₁₉	—	4	1	no	—
188	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₄²×C₁₉	—	2	2	no	—
192	C₄²×C₁₉	—	2	2	no	—
193	#10942	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	#117	1	1	yes	characteristic
197	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
198	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₁₉	#121	1	1	yes	characteristic
200	C₂³×C₁₉	#123	1	1	yes	characteristic
201	C₂³×C₁₉	#124	1	1	yes	characteristic
202	C₂³×C₁₉	#126	1	1	yes	characteristic
203	Q₈×C₁₉	—	2	4	no	—
204	Q₈×C₁₉	—	2	4	no	—
205	Q₈×C₁₉	—	4	2	no	—
206	Q₈×C₁₉	—	4	2	no	—
207	Q₈×C₁₉	—	4	2	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	8	2	no	—
223	C₂×C₄×C₁₉	—	8	2	no	—
224	C₂×C₄×C₁₉	—	8	2	no	—
225	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
253	C₈×C₁₉	—	2	2	no	—
254	C₈×C₁₉	—	2	2	no	—
255	C₈×C₁₉	—	2	4	no	—
256	C₈×C₁₉	—	4	2	no	—
257	C₈×C₁₉	—	4	2	no	—
258	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
259	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
260	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic
261	C₂×#405	C₂×C₁₉	1	1	yes	characteristic
262	C₂×#343	C₂×C₁₉	1	1	yes	characteristic
263	C₂×#341	C₂×C₁₉	1	1	yes	characteristic
264	#1736	C₂×C₁₉	1	1	yes	characteristic
265	C₂²×C₁₉	—	2	2	no	—
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	—	2	1	no	—
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×C₁₉	#386	1	1	yes	characteristic
275	C₂²×C₁₉	#388	1	1	yes	characteristic
276	C₂²×C₁₉	#388	1	1	yes	characteristic
277	C₂²×C₁₉	#388	1	1	yes	characteristic
278	C₂²×C₁₉	#388	1	1	yes	characteristic
279	C₂²×C₁₉	#390	1	1	yes	characteristic
280	C₂²×C₁₉	#471	1	2	yes	—
281	C₂²×C₁₉	#473	1	2	yes	—
282	C₄×C₁₉	—	4	4	no	—
283	C₄×C₁₉	—	4	4	no	—
284	C₄×C₁₉	—	8	2	no	—
285	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
286	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
287	C₄×C₁₉	#386	1	1	yes	characteristic
288	C₄×C₁₉	#386	1	1	yes	characteristic
289	C₄×C₁₉	#388	1	1	yes	characteristic
290	C₄×C₁₉	#388	1	1	yes	characteristic
291	C₄×C₁₉	#390	1	1	yes	characteristic
292	C₄×C₁₉	#390	1	1	yes	characteristic
293	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
294	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
296	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
297	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
300	#419	—	2	2	no	—
301	#419	C₄×C₁₉	1	4	yes	complemented
302	C₂×#103	—	2	2	no	—
303	C₂×#103	—	2	1	no	—
304	C₂×#103	—	2	1	no	—
305	C₂×#103	—	2	2	no	—
306	C₂×#103	C₄×C₁₉	1	4	yes	complemented
307	C₂×#101	—	2	2	no	—
308	C₂×#101	—	2	2	no	—
309	C₂×#101	C₄×C₁₉	1	4	yes	complemented
310	#405	—	2	2	no	—
311	#405	—	2	2	no	—
312	C₂×#97	—	2	1	no	—
313	C₂×C₄×C₈	—	2	1	no	—
314	#343	—	2	2	no	—
315	#341	—	2	2	no	—
316	#340	—	2	2	no	—
317	C₂×C₁₉	—	2	1	no	—
318	C₂×C₁₉	—	2	1	no	—
319	C₂×C₁₉	—	2	1	no	—
320	C₂×C₁₉	—	2	1	no	—
321	C₂×C₁₉	#1437	1	1	yes	characteristic
322	C₂×C₁₉	#1908	1	2	yes	—
323	C₂×C₁₉	#1930	1	2	yes	—
324	C₂×C₁₉	#1977	1	1	yes	characteristic
325	C₂×C₁₉	#1979	1	1	yes	characteristic
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	—	2	1	no	—
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×Q₈	—	2	1	no	—
330	C₂²×Q₈	—	2	1	no	—
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×Q₈	—	2	1	no	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×Q₈	—	2	1	no	—
337	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
338	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
339	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
340	C₂³×C₄	—	2	1	no	—
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
357	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
358	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
359	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
360	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
369	C₂²×C₈	D₄×C₁₉	1	2	yes	—
370	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
371	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	C₂×C₄×C₁₉	1	2	yes	—
375	#117	D₄×C₁₉	1	2	yes	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
382	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	#103	—	2	4	no	—
386	#103	—	2	4	no	—
387	#103	—	2	8	no	—
388	#101	—	2	8	no	—
389	#97	—	2	4	no	—
390	C₄×C₈	—	2	4	no	—
391	C₁₉	#10942	1	1	yes	characteristic, direct product factor, Sylow
392	C₂⁴	#41×C₁₉	1	1	yes	characteristic
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	4	1	no	—
409	C₂×Q₈	—	4	1	no	—
410	C₂×Q₈	—	4	1	no	—
411	C₂×Q₈	—	4	1	no	—
412	C₂×Q₈	—	4	1	no	—
413	C₂×Q₈	—	4	1	no	—
414	C₂×Q₈	—	4	1	no	—
415	C₂×Q₈	—	4	1	no	—
416	C₂×Q₈	—	4	1	no	—
417	C₂×Q₈	—	4	1	no	—
418	C₂×Q₈	—	4	1	no	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	C₄²×C₁₉	1	4	yes	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	4	1	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	8	2	no	—
433	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
444	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	4	1	no	—
455	M₁₆	—	4	1	no	—
456	M₁₆	—	4	1	no	—
457	M₁₆	—	4	1	no	—
458	M₁₆	C₂²⋊C₄×C₁₉	1	4	yes	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	4	1	no	—
473	C₂×C₈	—	4	1	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
477	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	C₁₉×#117	1	1	yes	characteristic
491	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
492	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
493	C₂³	C₁₉×#121	1	1	yes	characteristic
494	C₂³	C₁₉×#123	1	1	yes	characteristic
495	C₂³	C₁₉×#124	1	1	yes	characteristic
496	C₂³	C₁₉×#126	1	1	yes	characteristic
497	Q₈	—	2	4	no	—
498	Q₈	—	2	4	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	2	no	—
504	Q₈	—	4	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	C₂×C₄²×C₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
521	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
522	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
523	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
524	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
525	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
526	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
527	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
528	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
529	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
530	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
531	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
532	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
533	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
534	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
535	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
536	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
537	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
538	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
539	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
540	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
541	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
542	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
543	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
544	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
545	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
546	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	2	2	no	—
549	C₈	—	2	4	no	—
550	C₈	—	4	2	no	—
551	C₈	—	4	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
561	C₂²	C₁₉×#386	1	1	yes	characteristic
562	C₂²	C₁₉×#388	1	1	yes	characteristic
563	C₂²	C₁₉×#388	1	1	yes	characteristic
564	C₂²	C₁₉×#388	1	1	yes	characteristic
565	C₂²	C₁₉×#388	1	1	yes	characteristic
566	C₂²	C₁₉×#390	1	1	yes	characteristic
567	C₂²	C₁₉×#471	1	2	yes	—
568	C₂²	C₁₉×#473	1	2	yes	—
569	C₄	—	4	4	no	—
570	C₄	—	4	4	no	—
571	C₄	—	8	2	no	—
572	C₄	C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
573	C₄	C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
574	C₄	C₁₉×#386	1	1	yes	characteristic
575	C₄	C₁₉×#386	1	1	yes	characteristic
576	C₄	C₁₉×#388	1	1	yes	characteristic
577	C₄	C₁₉×#388	1	1	yes	characteristic
578	C₄	C₁₉×#390	1	1	yes	characteristic
579	C₄	C₁₉×#390	1	1	yes	characteristic
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	C₁₉×#1437	1	1	yes	characteristic
585	C₂	C₁₉×#1908	1	2	yes	—
586	C₂	C₁₉×#1930	1	2	yes	—
587	C₂	C₁₉×#1977	1	1	yes	characteristic
588	C₂	C₁₉×#1979	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator	C₂×C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
16. C₁₉×#419	C₄	semidirect
21. C₂×C₁₉×#103	C₄	semidirect
24. C₂×C₁₉×#101	C₄	semidirect
193. #10942	C₁₉	direct (N × H)
301. #419	C₄×C₁₉	semidirect
306. C₂×#103	C₄×C₁₉	semidirect
309. C₂×#101	C₄×C₁₉	semidirect
391. C₁₉	#10942	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#419	2
C₂²×C₁₉×#103	2
C₂²×C₁₉×#101	2
C₂×C₁₉×#405	2
C₂×C₁₉×#343	2
C₂×C₁₉×#341	2
C₁₉×#1736	2
#10942	19

Subgroups — C19×#10942 #18016901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10942 #18016901